Math SpringBoard Curriculum Map Algebra One Duration ____ Days Unit One Patterns and Equations Unit Overview Essential Questions Academic Vocabulary AP/College Readiness Students are introduced to fundamental concepts necessary for success in algebra by recognizing patterns and exploring real number sets, properties of operations, and properties of equality. Further into this unit, students will generate rules for solving simple linear equations and inequalities as well as rules for solving absolute value equations and inequalities. How are patterns, equations, and graphs related? Why are the properties of real numbers important when solving equations? variable distributive property equation solution compound inequality absolute value equation absolute value inequality Unit 1 develops concepts that engender a solid algebraic foundation by: • Developing pattern recognition necessary for success in AP Statistics. • Providing a constructivist approach to solving equations, enabling students to compare and evaluate multiple methods of solution. • Nurturing an understanding of properties of real numbers that contribute to the understanding of properties of functions necessary for success in AP Calculus. • Allowing for an intuitive understanding of absolute value and methods for solving
Transcript
Math SpringBoard Curriculum MapAlgebra One
Duration ____ DaysUnit One Patterns and Equations
Unit Overview Essential Questions Academic Vocabulary AP/College ReadinessStudents are introduced to fundamental concepts necessary for success in algebra by recognizing patterns and exploring real number sets, properties of operations, and properties of equality. Further into this unit, students will generate rules for solving simple linear equations and inequalities as well as rules for solving absolute value equations and inequalities.
How are patterns, equations, and graphs related?
Why are the properties of real numbers important when solving equations?
variable distributive property equation solution compound inequality absolute value equation absolute value
inequality
Unit 1 develops concepts that engender a solid algebraic foundation by:• Developing pattern recognitionnecessary for success in AP Statistics.• Providing a constructivist approach to solving equations, enabling students to compare and evaluate multiple methods of solution.• Nurturing an understanding ofproperties of real numbers thatcontribute to the understanding of properties of functions necessary forsuccess in AP Calculus.• Allowing for an intuitive understanding of absolute value and methods for solving equations and inequalities involving absolute value
SpringBoard Activities Content Focus Focus Standards and Learning Objectives
Comments
1.1 Investigating PatternsFor Love of the Game
• Numeric and graphicrepresentations of data• Linear vs. non-linear data• Pattern recognition• Predictions based on patterns
Students will be able:
-Recognize patterns.
-Make predictions after organizing given data.
-Write expressions using variables.
-Interpret data from given
-Simple Pattern Warmup-Homework within unit/2-5 problems in the unit-3 day timeframe-Exit slips last problem covered in day/additional generated problem/term review/written response-Check for understanding used as quiz possibly/use as formative if needed
representation (graph/chart/table).
-Recognize the difference between linear and non-linear graphs.
-Check your understanding/online problems/end of unit homework possibilities
1.2 Real NumbersGet Real
• Subsets of the real numbers• Relationship between subsets of the real numbers• Representations of rational numbers
Students will be able to:-create subsets of real numbers-determine and describe the relationships of real numbers-Determine and describe rational numbers in many forms of representations.
-Blackline Master cards for each student-3 day timeframe-Warmup/Number Sense-Homework problems in unit/online/CYU
1.3 Properties of Real NumbersProperties by the Pound
Students will be able to:-Define and apply properties of real numbers(Commutative/Associative/DistributiveInverse/Reflexive/Symmetric/Transitive)
- Homework problems in unit/online/CYU-2 day timeframe-Warmup/Visual representation of Commutative property
EA 1 Multiple Representations of DataShooting Stars
• Multiple representations of data• Linear versus non-linear data• Pattern recognition andprediction based on patterns
Students will be able to:-Recognize patterns.-Make predictions after organizing given data-Write expressions using variables-Interpret data from given representation (graph/chart/table)-Recognize the difference between linear and non-linear graphs-Create subsets of real numbers-Determine and describe the relationships of real numbers-Determine and describe rational numbers-Define and apply properties of real numbers(Commutative/Associative/DistributiveInverse/Reflexive/Symmetric/Transitive)- Give at least three correct predictions- Model a correct expression for given data and compare against a second representation.
-1 day timeframe-Warmup/Questioning on unit topics-Debriefing of previous material to activate prior knowledge-Students complete Embedded Assessment individually or as a group for grade
1.4 Solving Equations with ModelsWhat’s My Number?
• Multiple representations of data
Students will be able to:-Solve equations using various methods.
-3 day timeframe-Blackline Master 2 or algebra
• Linear versus non-linear data• Pattern recognition andprediction based on patterns
-Create equations based on given data tiles-Warmup/One variable equation-Index cards for “Whats my number” game.
• Solving multi-step equationswith algebraic methods• Solving equations with variables on both sides
Students will be able to:-Solve multi-step equations-Describe in written form the steps needed to solve and equation-Solve equations with variables on both sides
-4 day timeframe-Close Reading/Marking the TextWarmup/Equations-Quickwrite to assess student knowledge of procedures to solve equations
EA 2 Properties and Solving EquationsChecking Group Work
• Solving multi-step equations• Properties of numbers• Solution of an equation
Students will be able to:-Solve multi-step equations-Solve equations with variables on both sides-Define and apply properties of real numbers(Commutative/Associative/DistributiveInverse/Reflexive/Symmetric/Transitive)-Check solutions and conduct error analysis if needed
-1 day timeframe-Model-Students complete individually/group-Simulation for correcting student work
1.6 Solving InequalitiesPhysical Fitness Zones
• Solving and graphingone-variable inequalities• Compound Inequalities
Students will be able to:-Solve and graph one-variable equations-Recognize and graph Inequalities-Verify solutions to determine if inequality is true-Compare and contrast graphs of inequalities, and record data in a tabular format-Break down compound inequalities and find common solutions
-3/4/5 day timeframe-Warmup/Inequalities-Mini-Lessons to verify solutions-Have students write explanations when comparing solution methods-Large amount of Vocabulary terms that may be confusing, consider using a vocabulary organizer or interactive word wall
1.7 Absolute ValueStudent Distances
• Absolute value• Absolute value equations andInequalities
Students will be able to:-Determine absolute value-Create and solve absolute value inequalities -Solve absolute value equation with number line representation
-Warmup – Absolute Value/Inequalities-2 day timeframe-Opportunity for a movement activity as students represent places on the number line
EA 3 Inequalities and Absolute ValueA Healthy Pool
• Writing and solving inequalities• Solving absolute valueinequalities
Students will be able to:- Create and solve absolute value inequalities -Solve absolute value equation with number line representation
-Model-Debrief and Discuss activity-Work individually/group-Activate and assess number line knowledge
Assessment and Performance Opportunities Additional Resources Teacher Reflection
Check Your UnderstandingUnit PracticeUnit Reflection
SB Online Unit Assessment
In class questioning of studentsMonitoring of collaborative groups
Algebra Tiles, Index cards, Whiteboards Use problems in text, and suggested problems from each activity for homework.
Quiz after each activity if needed.
Test and review can be found online.
Make extensive use of “Getting Ready” Activities.
Assess prior knowledge of topics extensively before diving into unit.
Math SpringBoard Curriculum MapAlgebra 1
Duration ____ DaysUnit Two: Linear Functions
Unit Overview Essential Questions Academic Vocabulary AP/College ReadinessIn this unit, students study functions, in particular linearfunctions, function concepts including domain, range,y-intercept, x-intercept, or the zero of a function, and whatit means for a function to be continuous or discontinuous.Students represent functions in multiple ways. Most studentscome to Algebra 1 already familiar with linear patterns andan informal sense of the functional relationship betweentwo quantities. This unit formalizes much of that knowledge.Students write linear equations in various forms given a pointand a slope, two points, a table of values, or a graph. Theywrite algebraic models for verbal situations that exhibit aconstant rate of change, direct variation, and inverse variationusing multiple representations. The unit includes two activitieswith collected data where students write and use atrend-line to solve problems.
How can you showmathematical relationships?
Why are linear functionsuseful in real-worldsettings?
dependent variable direct variation domain function independent variable inverse variation linear equation range x-intercept y-intercept
Unit 2 continues to hone student understanding of function and the behavior of linear functions in particular by:• Formalizing the language of functions (e.g. domain, range, discrete, continuous).• Emphasizing writing and graphing linear functions given different conditions (slope-intercept, point-slope, x- and y-intercepts, two points).• Making the connection that the slope of a line represents a constant rate-of-change.• Exploring functions and linear functions and their behavior in a variety of ways: numerical, graphical, analytical, and verbal.• Modeling a written description of asituation with a linear function.• Collecting data based on a writtendescription of a situation and modeling the situation with a linear function.• Communicating their understanding verbally and in writing in a variety of situations both formally and informally.
SpringBoard Activities Content Focus Focus Standards and Learning Objectives
Comments
2.1 Introduction of FunctionVending Machines
• Concept of relation and function• Representations of functions
Students will be able to:-Determine whether a given
Getting Ready pg 66 before unit starts
• Function notation relation is a function.-Recognize the different representations of functions-Write in correct function notation-Determine the domain and range of a function.-Use a function machine to get ordered pairs
-4/5 day time frame-Warmup – Getting ready activity-Examine the presence of domain and range in a real world context-Use student response and examples to determine the understanding level of function notation.
2.2 Domain and Range of Continuous FunctionShake, Rattle, Roll
• Domain and range ofcontinuous functions• Set notation• Vertical line test
Students will be able to:-Differentiate between independent and dependent variables-Differentiate and represent the between continuous and discrete data-Determine the domain and range of continuous functions-Complete a vertical line test-Read Set Notation
-Warmup – Getting ready activity-3 day timeframe-Whiteboards/Chart Paper/Graphing Calculators-Use Group Discussion and Marking the Text strategies for long reading problems
2.3 Slope as Rate of ChangeRamp It Up
• Slope as a rate of change• Slope formula• Equivalent ratios• Linear models• Linear models to makepredictions
Students will be able to:-Determine slope-Determine rate of change using slope-Recognize and use equivalent ratios-Use linear models for analysis and prediction
-Warmup – Getting ready activity-Rulers-5 day timeframe-Large amounts of fraction work
EA1Bryce Canyon Hiking
• Definition of function• Representations of functions• Function notation
Students will be able to:-Determine the domain and range of given data-Define and create functions-Recognize different representations of functions
-Warmup – Getting ready activity-Quick review of needed ideas
-Write in correct function notation
2.4 Building a Linear ModelStacks of Cups
• Linear functions• Data collection• Pattern recognition• Slope as a rate of change• Writing equations
Students will be able to:-Collect and organize data-Recognize patterns-Recognize slope as a rate of change-Write equations with given data-Create equations based on organized data
-Warmup – Getting ready activity-Paper cups-Rulers-4 day timeframe-Students will have to visualize three dimensional models-RAFT
2.5 Direct and Inverse VariationStacking Boxes
• Direct variation• Inverse variation• Writing equations
Students will be able to:-Write equation for given data-Distinguish between inverse and direct variation and constant variation
-Warmup – Getting ready activity-Use empty boxes-2/3/4 day timeframe
EA2 Linear Functions and EquationsText Message Plans
• Discrete linear functions• Writing linear equations• Tabular and graphicalrepresentations• Domain and range• Comparison of y-values• Direct and inverse variation
Students will be able to:-Write Linear functions-Create graphical representations of linear functions-Determine domain and range-Compare y-values-Distinguish between inverse and direct variation
-Warmup – Getting ready activity-1 day timeframe-Debrief/Model/Individual or groups-Create Representation
2.6 Slope-Intercept FormWorking Under Pressure
• Slope-intercept form• Point-slope form• Standard Form• y-intercept• Linear models to makepredictions
Students will be able to:-Write equations in slope intercept form/point slope form/standard form-Find slope and y intercept-Use linear models to make predictions
-Warmup – Getting ready activity-5-7 timeframe-Possibly use mini-lessons with homework from additional sources-Review of pertinent information
2.7 x and y-interceptsCrossing the Axes
• x- and y-intercepts• Intercept form• Zero of a function
Students will be able to:-Find x and y intercepts-Write equations in intercept
-Warmup – Getting ready activity-Whiteboard or Chart Paper-2/3 day timeframe
form-Find the zeroes of a function
2.8 Equations form DataPass the Book
• Linear functions• Data collection• Represent data as a scatter plot• Analyze data using a trend line• Writing equations given 2 points• Interpreting slope and meaning of variable in context
Students will be able to:-Determine whether or not data is linear (via graph)-Create a scatterplot and draw a trend line-Explain correlations-Write and equation when given two points-Interpreting slope and variables in a real world context
-Warmup – Getting ready activity-3 day timeframe-Stopwatch-Whiteboard-Graph paper and calculator
EA3 Linear Equations and Slope as Rate of ChangeA 10K Run
• Linear functions• Writing linear equations• Slope as a rate of change• Domain
Students will be able to:-Write linear functions-Find slope, domain and range-Create a linear model-Find y intercept
-Warmup – Getting ready activityDebrief/Model/Individual or groups
Assessment and Performance Opportunities Additional Resources Teacher Reflection
Check Your UnderstandingUnit PracticeUnit Reflection
SB Online Unit Assessment
In class questioning of studentsMonitoring of collaborative groups
-Stopwatch-Whiteboard-Graph Paper-Calculator
Use problems in text, and suggested problems from each activity for homework.
Quiz after each activity if needed.
Test and review can be found online.
May need outside resources for Mini-Lessons.
Math SpringBoard Curriculum MapAlgebra 1
Duration ____ DaysUnit Three: Extensions of Linear Concepts
Unit Overview Essential Questions Academic Vocabulary AP/College ReadinessIn prior units, students have learned to analyze patterns, solve multi-step equations, and investigate linear functions. This unit continues the study of linear concepts by introducing students to piece-wise linear functions, inequalities with one and two variables, and systems of linear equations and inequalities.
Why would you use multiplerepresentations of linearequations and inequalities?
How are systems of linearequations and inequalitiesuseful in interpreting realworld situations?
Substitution Method Elimination Method Linear inequality Piecewise defined
function System of linear
equations System of linear
inequalities
Unit 3 continues to develop the algebra and graphing of functions and extends student understanding of the properties and language of piecewise functions by:• Providing contextual situations where linear and piecewise functions can be applied as required in the prerequisite topic list of AP Calculus.• Giving students opportunities to work with functions in a variety of ways: graphical, numerical, analytical, verbal.• Modeling a written description of aphysical situation with a function.• Allowing students to communicatemathematics and explain solutions both verbally and in written form.• Using technology to solve problems, experiment, interpret results, and support conclusions.
SpringBoard Activities Content Focus Focus Standards and Learning Objectives
Comments
3.1 Piecewise Linear FunctionBreakfast for Bowser
• Piecewise defined functions• Linear functions• Inequalities• Domain/range• Proportional reasoning
Students will be able to:-Create Expression based on tabular data-Understand and utilize piecewise functions-Make assumes based on proportional reasoning-Alter assumptions based on
-Warmup – Getting ready activity-Shared reading approach-Suggested assignment pace for homework-4 day timeframe
new data3.2 Equations in two-variablesA Tale of a Trucker
• Inequalities• Linear functions• Domain/range
Students will be able to:-Give written explanation of graphical data-Create two variable equations based on graphical data-Use inequalities to determine interval of distances and solution areas
-Warmup – Getting ready activity-Use Connect to Business feature-3/4 day timeframe-Teach students how the graphs show solution areas-Graphing Calculator
3.3 Inequalities in two-variablesShared Minutes
• Inequalities• Linear functions• Graphing inequalities in two variables• Domain and range
Students will be able to:-Write linear inequality given tabular data-Determine full solution areas-Recognize if solution fall in an open or closed half plane-Solve and graph two variable inequalities
-Warmup – Getting ready activity1 to 2 day timeframeMini LessonsInteractive Word Wall
EA1 Graphing Inequalities and Piecewise FunctionsEarnings on a Graph
• Writing linear inequalities• Graphing linear inequalities• Writing piecewise definedfunctions• Graphing piecewise definedfunctions
Students will be able to:-Write and graph linear inequalities and piecewise functions
-Warmup – Getting ready activity-Review of needed material
3.4 Parallel and Perpendicular linesThe Slope of Things
• Relationship between the slopes of parallel and perpendicular lines.
Students will be able to:-Differentiate between parallel and perpendicular by examining slopes
-Warmup – Getting ready activity-2/3 days
3.5 System of Linear EquationsA Tale of Two Truckers
• Writing algebraic expressions and equations• Solving systems of linearequations graphically,numerically and algebraically• Revisiting A Tale of a Trucker scenario from Activity 3.2
Students will be able to:-Solve systems of equations in various methods-Compare and contrast different solution methods
3.6 Solving systems of linear equationsWhat’s in the Mix?
• Solving systems of linearequations by elimination (linear combination) and substitution• Identifying types of solutions to a system of linear equations• Solving systems with three variables
Students will be able to:-Solve systems of linear equations by elimination and substitutions-Classify the systems of equations (e.g. dependent/consistent)
-Warmup – Getting ready activity-2/3 days
3.7 Systems of linear InequalitiesWhich Region Is It?
• Systems of linear inequalities• Concept of solution of a system of linear inequalities• Finding solutions of systems of linear inequalities by graphing
Students will be able to:-Find solution set with multiple inequalities
-Warmup – Getting ready activity-2 days-Graph Paper-Review of open or closed solution areas
EA2 Systems of Equations and InequalitiesAll Systems Go
• Representing problem situations with systems of linear equations• Using multiple methods to solve systems of equations• Solving systems of linearinequalities
Students will be able to:-Write correct systems of equations and inequalities-Define system variables
-Warmup – Getting ready activity-Group assignment
Assessment and Performance Opportunities Additional Resources Teacher Reflection
Embedded Assessment 1Embedded Assessment 2
Check Your UnderstandingUnit PracticeUnit Reflection
SB Online Unit Assessment
In class questioning of studentsMonitoring of collaborative groups
-Supplemental resources (Graphing)-Possibly additional homework questions from springboard online or outside source
Use problems in text, and suggested problems from each activity for homework.
Quiz after each activity if needed.
Test and review can be found online.
May need outside resources for Mini-Lessons
Preassessment of student with coordinate graphing
Math SpringBoard Curriculum MapAlgebra 1
Duration ____ DaysUnit Four: Exponents, Radicals, and Polynomials
Unit Overview Essential Questions Academic Vocabulary AP/College ReadinessIn prior units students have looked at linear and nonlinear patterns and extended the linear concepts to functions, inequalities, and piece-wise defined functions. This unit changes focus and moves students to explore exponent rules and functions, and extends into operations with radical, and polynomial functions and operations. This unit concludes with an introduction to rational expressions.
How do multiplicative patternsmodel the physical world?
How are adding andmultiplying polynomialexpressions different fromeach other?
coefficient degree of a polynomial difference of two
squares factor polynomial radical expression rational expression term
Unit 4 expands on students’understanding of the concept of rateof change and develops the properties, language, and algebra of some nonlinear functions by:• Providing contextual situationsdealing with exponential functions,polynomial functions, and radical and rational expressions as required in the prerequisite topic list for AP Calculus.• Giving students the opportunity to look at exponential and polynomial functions graphically, numerically, algebraically, and verbally, both in and out of contextual situations.• Allowing students to compare andcontrast rates of change of nonlinearfunctions with the constant rates ofchange of linear functions.• This unit builds students’ facility with manipulation and computational competence, while extending the conceptual understanding of broad concepts.
SpringBoard Activities Content Focus Focus Standards and Learning Objectives
Comments
4.1 Exponents RulesIcebergs and Exponents
• Exponent rules• Scientific notation• Meaning of negative exponents• Meaning of a number to a zero power
Students will be able to:-Write in correct scientific notation-Know correct exponent rules for each situation-Know how to manipulate negative exponent, and zero
-Warmup: Created flashback or getting ready activity-3/4 days-Extensive use of tables-Use Suggested Assignment for Homework setup
power exponents-Use power of Product/Quotient property to make predictions
4.2 Exponential FunctionsProtecting Your Investment
• Introduction to exponential functions• Multiplicative patterns• Representations of non-linear data• Predictions using exponential functions
-Predict values using the exponential function-Use ratios to determine multiplicative patterns-Understand concepts of Exponential growth and decay
Warmup: Created flashback or getting ready activity-3 to 4 days
-Reflect on pacing-Use of BLM-Use CYO for formative assessments
SB Online Unit Assessment
In class questioning of studentsMonitoring of collaborative groups
Math SpringBoard Curriculum MapAlgebra 1
Duration ____ DaysUnit Five: Quadratic Functions
Unit Overview Essential Questions Academic Vocabulary AP/College ReadinessQuadratic equations and functions are the focus of this unit. The unit opens with students modeling a quadratic function from a verbal description numerically, graphically, and algebraically. Students learn to graph quadratics using transformations of the parent function f (x) = x 2 and are able to identify key features of quadratic functions. They solveequations using a variety of methods and finish the unit by modeling physical situations with quadratic relationships.
How are quadratic functionsused to model, analyze and interpret mathematicalrelationships?
Why is it advantageous to know a variety of ways to solve and graph quadraticfunctions?
parabola parent function quadratic formula quadratic function real roots of an equation transformation vertex of a parabola
In Unit 5, students are provided with a family of functions whose rate of change is not constant but whose behavior is none-the-less predictable and seen often in Advanced Placement mathematics. This unit helps prepare students for Advanced Placement courses by• Modeling motion using quadraticrelationships.• Writing equations from verbaldescriptions and physical models.• Making connections between multiple ways to represent mathematical information: numerically, graphically, verbally and algebraically.• Increasing student ability to solve awide-variety of equations and to choose the most appropriate solution method when needed.• Using technology as a tool fordiscovering relationships, testingconjectures, and solving problems
SpringBoard Activities Content Focus Focus Standards and Learning Objectives
Comments
5.1 Introduction to Quadratic FunctionsTouchlines
• Introduction to quadraticfunctions• Multiple representations of quadratic data
Students will be able to:-Understand the components of the quadratic function-Recognize the graphical and tabular representations of the quadratic function
Warmup: Created flashback or getting ready activity-extended focus on word wall
5.2 Graphing y=ax2+c
Transformers
• Define parent function• Transform graphs of y = x2 by introducing a and c iny = ax2+ c• Distinguish amongtransformations
Students will be able to:-Define parent function-Write a quadratic function related to a given graph-Recognize how adding the constant transform the graph-Distinguish among transformations
Warmup: Created flashback or getting ready activity-4 days-cover vertical/horizontial stretch/shrink ideas
EA1 Graphing QuadraticsQuadratic Introduction
• Graph quadratic functions with transformations of the form y = a x2 + c• Identify quadratic functions by recognizing characteristics of different representations
Students will be able to:-Graph quadratic functions with transformations-Explain method used to graph function
Warmup: Created flashback or getting ready activity-understand minimum and maximum vertex
5.3 Solving quadratic equationsTrebuchet Trials
• Solving quadratic equationsby factoring• Connecting real roots of a quadratic equation to thex-intercepts of the relatedfunction graph• Graphing quadratic functions using the vertex and zeros
Students will be able to:-Factor quadratic equations to find solutions-Find x-int and find zero of the function, and graph functions-Understand connections between solution, x-int, zeros
Warmup: Created flashback or getting ready activity-interdisciplinary mini-lessons-solution confirmation as an AP skill
5.4 Solving Quadratic EquationsKeeping It Quadratic
• Solving quadratic equations by taking a square root, completing the square, and the quadratic formula.• The discriminant and the nature of the roots of a quadratic equation
Students will be able to:-Solve quadratic by completing the square and quadratic formula-Use discriminant to determine number of roots for any quadratic equation
Warmup: Created flashback or getting ready activity-Use calculator to evaluate square roots-Use estimation skills
5.5 Applying quadratic EquationsRockets In Flight
• Solving problems that involve quadratic functions• Solving quadratic equations including piecewise definedfunctions
Students will be able to:-Use quadratic function to solve real world problems-Use quadratic function to determine rate of change (length of time)
Warmup: Created flashback or getting ready activity-4 days- Graphing calculators
EA2 Solving Quadratic EquationsEgg Drop
• Modeling and solving quadratic equations
Students will be able to:-Model and solve quadratic equations in an interdisciplinary real world situation-Determine best method for solving the problem (graphing, factoring , square roots)
Warmup: Created flashback or getting ready activity-Activation of prior knowledge
Assessment and Performance Opportunities Additional Resources Teacher Reflection
Embedded Assessment 1Embedded Assessment 2
Check Your UnderstandingUnit PracticeUnit Reflection
SB Online Unit Assessment
In class questioning of studentsMonitoring of collaborative groups
Graphing calculator/paper optional -Reflect on pacing-Use of BLM-Use CYO for formative assessments-Use problems in text, and suggested problems from each activity for homework.-Quiz after each activity if needed.-Test and review can be found online.-May need outside resources for Mini-Lessons
Math SpringBoard Curriculum MapAlgebra 1
Duration ____ DaysUnit Six: Data Analysis and Surveys
Unit Overview Essential Questions Academic Vocabulary AP/College ReadinessIn prior levels, students have learned the basic concepts of measures of center, plotting data, and sampling bias. This unit continues the study of statistics with a deeper look at center and spread, measurement and sampling errors, sources of bias in the collection and representations of data, and the process of developing a survey.
How do sampling methods affect the evaluation of surveyresults?
How can displays andsummaries be used to interpret and communicate the results of surveys?
bias categorical variable census five-number summary margin of error mean absolute deviation quantitative variable sample simple random sample
Unit 6 extends student understanding of statistics by:• Providing contextual situations where data measures can be calculated and displayed in a variety of ways: measures of central tendency and spread, box-and- whisker plots, stem-and-leaf plots, and scatterplots.• Giving students opportunities to work with data collection and representation both in analyzing news articles and developing a survey.• Allowing students to communicatemathematically and explain surveyresults both verbally and in writtenform.• Using technology to solve problems, experiment, interpret results, and support conclusions.• Learning and using the vocabulary of statistics.
SpringBoard Activities Content Focus Focus Standards and Learning Objectives
Comments
6.1 Measure of Center and SpreadTo Text or Not to Text?
• Center and spread of data• Mean absolute deviation• Sample and census• Sampling and measurementerror• Stem-and-leaf plots
Students will be able to:-Find measures of central tendency-Distinguish between population/sample/census-Create and use Stem and Leaf plots-Recognize Bias
Warmup: Created flashback or getting ready activity-Get quick understanding of student levels on measures of central tendency-2 days
6.2 Random samples and EstimationHow Old Are These Coins?
• Five-number summary• Quartiles• Box-and-whisker plots• Simple random samples• Using a random number table• Analyzing and comparing means of sample and populations
Students will be able to:-Understand and create box and whisker plots-Understand five number summary used to create box and whisker plots-Collect data using a random number table-Compare the means of samples and populations
Warmup: Created flashback or getting ready activity-3 days-Interactive Word Wall
EA1 Inferences Based on DataPlots and Sampling
• Stem-and-leaf plot• Box-and-whisker plot• Five-number summary• Mean absolute deviation• Random number table• Sampling and measurementerror
Students will be able to:- Find measures of central tendency-Distinguish between population/sample/census-Create and use Stem and Leaf plots-Understand and create box and whisker plots-Understand five number summary used to create box and whisker plots-Collect data using a random number table-Compare the means of samples and populations
Warmup: Created flashback or getting ready activity
6.3 SamplingWhat’s the Mean?
• Sample selection• Stratified random sample• Convenience sample• Mean• Bias
Students will be able to:-Recognize Bias-Compare the means of given data-Distinguish between sample methods
Warmup: Created flashback or getting ready activity-2 days
6.4 Developing a SurveyThe Race is On!
• Surveys in the media• Bias in surveys• Truncated scales on graphs
Students will be able to:-Understand and use surveys in a context- Understand margin for error on surveys and graphical representation
Warmup: Created flashback or getting ready activity-Use as many real world applications as possible/media
-See how bias can create unreliable data and representations
6.5 Conducting a SurveyThey’re Gr8!
• Writing survey questions• Question of interest• Categorical and quantitative variables• Making graphs of data
Students will be able to:-Write survey questions/question of interest-Decipher or determine the difference between categorical and quantitative variables-Create various of representations of data
Warmup: Created flashback or getting ready activity-Students complete surveys in small groups
Students will be able to:-Identify more than one type of bias-Write relevant survey questions-Choose appropriate method to conduct survey-Choose appropriate representation
Warmup: Created flashback or getting ready activity
Assessment and Performance Opportunities Additional Resources Teacher Reflection
Embedded Assessment 1Embedded Assessment 2
Check Your UnderstandingUnit PracticeUnit Reflection
SB Online Unit Assessment
In class questioning of studentsMonitoring of collaborative groups
Supplemental materialsNewspaper survey dataReal world Sample data
-Use CYO for formative assessments-Use problems in text, and suggested problems from each activity for homework.-Quiz after each activity if needed.-Test and review can be found online.-May need outside resources for Mini-Lessons-Great section for real world application
